A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

Jiao, J., Trentelman, H. L. & Camlibel, M. K., Mar-2020, In : IEEE Transactions on Automatic Control. 65, 3, p. 1218-1225 8 p., 8736845.

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  • A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

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This note is concerned with a suboptimal version of the distributed linear quadratic optimal control problem for multiagent systems. Given a multiagent system with identical agent dynamics and an associated global quadratic cost functional, our objective is to design distributed control laws that achieve consensus and whose cost is smaller than an a priori given upper bound, for all initial states of the network that are bounded in norm by a given radius. A centralized design method is provided to compute such suboptimal controllers, involving the solution of a single Riccati inequality of dimension equal to the dimension of the agent dynamics, and the smallest nonzero and the largest eigenvalue of the Laplacian matrix. Furthermore, we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the Laplacian matrix by using only lower and upper bounds on these eigenvalues. Finally, a simulation example is provided to illustrate our design method.

Original languageEnglish
Article number8736845
Pages (from-to)1218-1225
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - Mar-2020


  • Optimal control, Multi-agent systems, Eigenvalues and eigenfunctions, Laplace equations, Symmetric matrices, Upper bound, Design methodology, Consensus, distributed control, linear quadratic optimal control, multiagent systems, suboptimality, COOPERATIVE OPTIMAL-CONTROL, MULTIAGENT SYSTEMS, SYNCHRONIZATION PROBLEMS, DIFFUSIVE COUPLINGS, CONSENSUS, DESIGN, NECESSITY, FEEDBACK, GRAPHS

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